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e-lub [12.9K]
3 years ago
8

What is the y-intercept of the line passing through the point 5, -6 with a slope of -1 over 7

Mathematics
1 answer:
morpeh [17]3 years ago
5 0

Answer:

  • The y-intercept is (0, -37/7).

Explanation:

When you have one point and the slope of a line you can find its equation by using the point-slope form of the linear function:

  • m = slope
  • point = (a, b)
  • point-slope equation: (y - b) = m (x - a).

Now substitute m = -1/7 and (a,b) = (5, - 6)

  • y - (-6) = -1/7 (x - 5)

Solve for y:

  • y + 6 = - 1/7 ( x - 5)
  • 7y + 7(6) = - (x - 5)
  • 7y + 42 = - x + 5
  • 7y = - x + 5 - 42
  • 7y = - x - 37
  • y = -(1/7)x - 37/7 ← this is the slope-intercept form of the equation.

The y-intercept is the point when x = 0. So, the corresponding y-coordinate is the constant term in the last equation:

  • y = 0 - 37/7 = - 37/7

And the y-intercept is the point (0, -37/7).

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Which point is on the graph of f(x) = 2*5^x
vodomira [7]

Answer:

Option B (1,10)

Step-by-step explanation:

we have

f(x)=2(5^x)

we know that

If a ordered pair is on the graph of f(x) then the ordered pair must satisfy the function f(x)

<u><em>Verify each case</em></u>

case A) (0,0)

For x=0

f(x)=2(5^0)\\f(x)=2(1)=2

Compare the value of f(x) with the y-coordinate of the ordered pair

2\neq 0

therefore

The ordered pair is not on the graph of f(x)

case B) (1,10)

For x=1

f(x)=2(5^1)\\f(x)=2(5)=10    

Compare the value of f(x) with the y-coordinate of the ordered pair

10=10

therefore

The ordered pair is on the graph of f(x)

case C) (0,10)

For x=0

f(x)=2(5^0)\\f(x)=2(1)=2

Compare the value of f(x) with the y-coordinate of the ordered pair

2\neq 10

therefore

The ordered pair is not on the graph of f(x)

case D) (10,1)

For x=10

f(x)=2(5^{10})\\f(x)=2(9,765,625)=19,531,250

Compare the value of f(x) with the y-coordinate of the ordered pair

19,531,250\neq 1

therefore

The ordered pair is not on the graph of f(x)

7 0
3 years ago
2) Solve the System of Equations using Substitution. (5 points) -3x+2y=12 x=2y-8
Tems11 [23]

Answer:

x= -2 and y= 3

Step-by-step explanation:

since x = 2y -8, substitute this in the first equation

Thus, -3(2y-8) + 2y =12

-6y+24+2y=12

-6y+2y=12-24

-4y=-12

y=3

put the value of y in the second equation,

x=2y-8

x=2(3)-8

x=6-8

x=-2

So, x=-2. y=3

5 0
3 years ago
Simplify: 3x^2-8x+4 and show work please
Bad White [126]

believe what you're asking is to turn the trinomial into two binomials

So you first have to get 3x²; the only way to get this is

(3x    )(x     )     when multiplying that, you would get 3x²

when dealing with the -8x and the 4, you must find numbers that are factors of four (when multiplied together they will equal 4) and will multiply with the x's to get -8

(3x-2)(x-2)

you can tell that this is the answer because when you multiply though you will get:

3x-2x²-6x+4

or: 3x²-8x_4

Hope this helped


5 0
3 years ago
Khan academy Find the median of the data in the dot plot below. chocolate chips
Helga [31]

Answer:

Where's the picture?

Step-by-step explanation:

Can't see it.

6 0
3 years ago
Please answer this correctly
larisa [96]
731.8, 730.63, 730.38, 730.1

Hope this helps!
3 0
3 years ago
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